发表机构
Syracuse University; Institute for Quantum & Information Sciences, Syracuse University（雪城大学; 雪城大学量子与信息科学研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文比较Redfield方程与Magnus重求和，证明弱耦合下非马尔可夫Redfield演化仍接近CPTP映射，并给出可靠性判据。
AI 中文摘要
具有时间依赖系数的Redfield方程（或TCL2方程）给出了从微观理论推导出的开放量子系统动力学的最简单的微扰描述之一。然而，其作为近似的地位是微妙的：虽然微扰理论在系统-环境耦合中逐阶固定了约化动力学，但求解Redfield方程会产生一种特定的重求和，该重求和不一定保持完全正性。在此，我们比较Redfield演化与同一二阶微扰映射的指数化（Magnus）重求和，后者在广泛的物理条件下是完全正且迹保持的（CPTP）。我们还构造了一个简单的CPTP resolvent重求和，说明了同一微扰映射的重求和的非唯一性。Redfield和Magnus方案在二阶上一致，但在高阶上通过时间排序修正而不同。我们展示了一个弱耦合准则，该准则保证Redfield演化，即使是非马尔可夫的，也保持接近CPTP映射。我们在两个例子中说明了该准则，重点关注有限维（量子比特）系统。我们的结果阐明了Redfield演化何时以及为何即使高度非Lindbladian也能保持可靠。
英文摘要
The Redfield equation with time-dependent coefficients (or TCL2 equation) gives one of the simplest perturbative descriptions of open quantum system dynamics derived from a microscopic theory. Its status as an approximation is nevertheless subtle: while perturbation theory fixes the reduced dynamics order-by-order in the system-environment coupling, solving the Redfield equation yields a particular resummation that need not preserve complete positivity. Here we compare Redfield evolution with an exponentiated (Magnus) resummation of the same second-order perturbative map, which is completely positive and trace preserving (CPTP) for a broad class of physical conditions. We also construct a simple CPTP resolvent resummation, illustrating the non-uniqueness of resummations of the same perturbative map. The Redfield and Magnus prescriptions agree to second order but differ through time-ordering corrections at higher orders. We exhibit a weak-coupling criterion which guarantees that Redfield evolution, even when non-Markovian, remains close to a CPTP map. We illustrate the criterion in two examples, focusing on finite-dimensional (qubit) systems. Our results clarify when, and why, Redfield evolution can remain reliable even when it is highly non-Lindbladian.
Comments18 pages + appendices; 4 figures
